DASSO: connections between the Dantzig selector and lasso
DASSO: connections between the Dantzig selector and lasso
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DOI：
10.1111/j.1467-9868.2008.00668.x
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发表时间：
2009-01-01
影响因子：
5.8
通讯作者：
Lv, Jinchi
中科院分区：
文献类型：
--
作者：
James, Gareth M.;Radchenko, Peter;Lv, Jinchi
我们提出了一种新的算法，DASSO，用于拟合的Dantzig选择器的整个系数路径，具有类似的计算成本的最小角度回归算法，用于计算套索。DASSO通过一个类似于最小角度回归算法的序列单纯形算法有效地构造了一条分段线性路径。这两种算法的比较揭示了套索和Dantzig选择器如何相关的问题。此外，我们还提供了设计矩阵X的理论条件，在此条件下，对于某些调谐参数，套索和Dantzig选择器系数估计值将相同。因此，在许多情况下，我们可以将Dantzig选择器的强大的非渐近界扩展到套索。最后，通过模拟和真实的世界的数据集的实证研究，我们表明，在实践中，当范围举行的Dantzig选择器，他们几乎总是也举行套索。
We propose a new algorithm, DASSO, for fitting the entire coefficient path of the Dantzig selector with a similar computational cost to the least angle regression algorithm that is used to compute the lasso. DASSO efficiently constructs a piecewise linear path through a sequential simplex-like algorithm, which is remarkably similar to the least angle regression algorithm. Comparison of the two algorithms sheds new light on the question of how the lasso and Dantzig selector are related. In addition, we provide theoretical conditions on the design matrix X under which the lasso and Dantzig selector coefficient estimates will be identical for certain tuning parameters. As a consequence, in many instances, we can extend the powerful non-asymptotic bounds that have been developed for the Dantzig selector to the lasso. Finally, through empirical studies of simulated and real world data sets we show that in practice, when the bounds hold for the Dantzig selector, they almost always also hold for the lasso.